By QB365 on 31 Dec, 2022
QB365 provides a detailed and simple solution for every Possible Questions in Class 12 Maths Subject - Important 1 Mark MCQ's, English Medium. It will help Students to get more practice questions, Students can Practice these question papers in addition to score best marks.
12th Standard
Maths
Answer all the following Questions.
If |adj(adj A)| = |A|9, then the order of the square matrix A is
3
4
2
5
If A is a 3 \(\times\) 3 non-singular matrix such that AAT = ATA and B = A-1AT, then BBT =
A
B
I3
BT
The conjugate of a complex number is \(\cfrac { 1 }{ i-2 } \). Then the complex number is
\(\cfrac { 1 }{ i+2 } \)
\(\cfrac { -1 }{ i+2 } \)
\(\cfrac { -1 }{ i-2 } \)
\(\cfrac { 1 }{ i-2 } \)
If \(z=\cfrac { \left( \sqrt { 3 } +i \right) ^{ 3 }\left( 3i+4 \right) ^{ 2 } }{ \left( 8+6i \right) ^{ 2 } } \) , then |z| is equal to
0
1
2
3
According to the rational root theorem, which number is not possible rational zero of 4x7 + 2x4 - 10x3 - 5?
-1
\(\frac { 5 }{ 4 } \)
\(\frac { 4 }{ 5 } \)
5
The polynomial x3 - kx2 + 9x has three real zeros if and only if, k satisfies
|k| ≤ 6
k = 0
|k| > 6
|k| ≥ 6
\(\sin ^{-1} \frac{3}{5}-\cos ^{-1} \frac{12}{13}+\sec ^{-1} \frac{5}{3}-\operatorname{cosec}^{-1} \frac{13}{12}\) is equal to
2\(\pi\)
\(\pi\)
0
tan-1\(\frac{12}{65}\)
If sin−1x = 2sin−1 \(\alpha\) has a solution, then
\(|\alpha |\le \frac { 1 }{ \sqrt { 2 } } \)
\(|\alpha |\ge \frac { 1 }{ \sqrt { 2 } } \)
\(|\alpha |<\frac { 1 }{ \sqrt { 2 } } \)
\(|\alpha |>\frac { 1 }{ \sqrt { 2 } } \)
The circle x2 + y2 = 4x + 8y +5 intersects the line 3x−4y = m at two distinct points if
15< m < 65
35< m <85
−85 < m < −35
−35 < m < 15
The length of the diameter of the circle which touches the x - axis at the point (1, 0) and passes through the point (2, 3).
\(\frac { 6 }{ 5 } \)
\(\frac { 5 }{ 3 } \)
\(\frac { 10 }{ 3 } \)
\(\frac { 3 }{ 5 } \)
If \(\vec { a } ,\vec { b } ,\vec { c } \) are three unit vectors such that \(\vec { a } \) is perpendicular to \(\vec { b } \) and is parallel to \(\vec { c } \) then \(\vec { a } \times (\vec { b } \times \vec { c } )\) is equal to
\(\vec { a } \)
\(\vec { b} \)
\(\vec { c } \)
\(\vec { 0 } \)
If \([\vec{a}, \vec{b}, \vec{c}]=1\), then the value of \(\frac{\vec{a} \cdot(\vec{b} \times \vec{c})}{(\vec{c} \times \vec{a}) \cdot \vec{b}}+\frac{\vec{b} \cdot(\vec{c} \times \vec{a})}{(\vec{a} \times \vec{b}) \cdot \vec{c}}+\frac{\vec{c} \cdot(\vec{a} \times \vec{b})}{(\vec{c} \times \vec{b}) \cdot \vec{a}}\) is
1
-1
2
3
A stone is thrown up vertically. The height it reaches at time t seconds is given by x = 80t -16t2. The stone reaches the maximum height in time t seconds is given by
2
2.5
3
3.5
The point on the curve 6y = x3 + 2 at which y-coordinate changes 8 times as fast as x-coordinate is
(4, 11)
(4, -11)
(-4, 11)
(-4,-11)
If \(u(x, y)=e^{x^{2}+y^{2}}\),then \(\frac { \partial u }{ \partial x } \) is equal to
\(e^{x^{2}+y^{2}}\)
2xu
x2u
y2u
If v (x, y) = log (ex + ey), then \(\frac { { \partial }v }{ \partial x } +\frac { \partial v }{ \partial y } \) is equal to
ex + ey
\(\frac{1}{e^x + e^y}\)
2
1
If \(\frac{\Gamma(n+2)}{\Gamma(n)}=90\) then n is
10
5
8
9
The value of \(\int _{ 0 }^{ \frac { \pi }{ 6 } }{ { cos }^{ 3 }3x\ dx }\ is\)
\(\frac{2}{3}\)
\(\frac{2}{9}\)
\(\frac{1}{9}\)
\(\frac{1}{3}\)
The order and degree of the differential equation \(\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } +{ \left( \frac { dy }{ dx } \right) }^{ 1/3 }+{ x }^{ 1/4 }=0\) are respectively
2, 3
3, 3
2, 6
2, 4
The order and degree of the differential equation \(\sqrt { sinx } (dx+dy)=\sqrt { cos x } (dx-dy)\) is
1, 2
2, 2
1, 1
2, 1
A random variable X has binomial distribution with n = 25 and p = 0.8 then standard deviation of X is
6
4
3
2
If the function \(f(x)=\frac { 1 }{ 12 } \) for a < x < b, represents a probability density function of a continuous random variable X, then which of the following cannot be the value of a and b?
0 and 12
5 and 17
7 and 19
16 and 24
Subtraction is not a binary operation in
R
Z
N
Q
Which one of the following is a binary operation on N?
Subtraction
Multiplication
Division
All the above
In the last column of the truth table for ¬( p ∨ ¬q) the number of final outcomes of the truth value 'F' are
1
2
3
4
If |z1| = 1, |z2| = 2, |z3| = 3 and |9z1z2 + 4z1z3 + z2z3| = 12, then the value of |z1+z2+z3| is
1
2
3
4
If \(\frac { z-1 }{ z+1 } \) is purely imaginary, then |z| is
\(\frac { 1 }{ 2 } \)
1
2
3
If (1+i)(1+2i)(1+3i)...(1+ni) = x + iy, then \(2\cdot 5\cdot 10...\left( 1+{ n }^{ 2 } \right) \) is
1
i
x2+y2
1+n2
The volume of solid of revolution of the region bounded by y2 = x(a − x) about x-axis is
\(\pi a^3\)
\(\frac { \pi { a }^{ 3 } }{ 4 } \)
\(\frac { \pi { a }^{ 3 } }{ 5 } \)
\(\frac { \pi { a }^{ 3 } }{ 6 } \)
If \(\int _{ 0 }^{ x }{ f(t)dt=x+\int _{ x }^{ 1 }{ tf } (t)dt } \), then the value of f (1) is
\(\frac{1}{2}\)
2
1
\(\frac{3}{4}\)
The value of \(\int _{ -\frac { \pi }{ 2 } }^{ \frac { \pi }{ 2 } }{ { sin }^{ 2 }x\ cos \ x \ dx } \) is
\(\frac{3}{2}\)
\(\frac{1}{2}\)
0
\(\frac{2}{3}\)
Which one of the following statements has the truth value T?
sin x is an even function
Every square matrix is non-singular
The product of complex number and its conjugate is purely imaginary
\(\sqrt 5\) is an irrational number
Which one is the inverse of the statement (pVq)➝(pΛq)?
(p∧q)➝(pVq)
ᄀ(pvq)➝(p∧q)
(ᄀpvᄀq)➝(ᄀp∧ᄀq)
(ᄀp∧ᄀq)➝(ᄀpVᄀq)
Which one of the following is not true?
Negation of a negation of a statement is the statement itself
If the last column of the truth table contains only T then it is a tautology.
If the last column of its truth table contains only F then it is a contradiction
If p and q are any two statements then p↔️q is a tautology.
If A = \(\left[ \begin{matrix} 1 & \tan { \frac { \theta }{ 2 } } \\ -\tan { \frac { \theta }{ 2 } } & 1 \end{matrix} \right] \) and AB = I2, then B =
\(\left( \cos ^{ 2 }{ \frac { \theta }{ 2 } } \right) A\)
\(\left( \cos ^{ 2 }{ \frac { \theta }{ 2 } } \right) { A }^{ T }\)
\(\left( \cos ^{ 2 }{ \theta } \right) I\)
(Sin2\(\frac { \theta }{ 2 } \))A
The rank of the matrix \(\left[ \begin{matrix} 1 \\ \begin{matrix} 2 \\ -1 \end{matrix} \end{matrix}\begin{matrix} 2 \\ \begin{matrix} 4 \\ -2 \end{matrix} \end{matrix}\begin{matrix} 3 \\ \begin{matrix} 6 \\ -3 \end{matrix} \end{matrix}\begin{matrix} 4 \\ \begin{matrix} 8 \\ -4 \end{matrix} \end{matrix} \right] \) is
1
2
4
3
If (AB)-1 = \(\left[ \begin{matrix} 12 & -17 \\ -19 & 27 \end{matrix} \right] \) and A-1 = \(\left[ \begin{matrix} 1 & -1 \\ -2 & 3 \end{matrix} \right] \), then B-1 =
\(\left[ \begin{matrix} 2 & -5 \\ -3 & 8 \end{matrix} \right] \)
\(\left[ \begin{matrix} 8 & 5 \\ 3 & 2 \end{matrix} \right] \)
\(\left[ \begin{matrix} 3 & 1 \\ 2 & 1 \end{matrix} \right] \)
\(\left[ \begin{matrix} 8 & -5 \\ -3 & 2 \end{matrix} \right] \)
If x + y = k is a normal to the parabola y2 = 12x, then the value of k is
3
-1
1
9
Area of the greatest rectangle inscribed in the ellipse \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\) is
2ab
ab
\( \sqrt{ ab}\)
\(\frac { a }{ b } \)
The locus of a point whose distance from (-2,0) is \(\frac { 2 }{ 3 } \) times its distance from the line x = \(\frac { -9 }{ 2 } \) is
a parabola
a hyperbola
an ellipse
a circle
Let X be random variable with probability density function
\(f(x)=\left\{\begin{array}{ll} \frac{2}{x^{3}} & x \geq 1 \\ 0 & x<1 \end{array}\right.\)
Which of the following statement is correct
both mean and variance exist
mean exists but variance does not exist
both mean and variance do not exist
variance exists but Mean does not exist
A balloon rises straight up at 10 m/s. An observer is 40 m away from the spot where the balloon left the ground. The rate of change of the balloon's angle of elevation in radian per second when the balloon is 30 metres above the ground.
\(\frac{3}{25} \text { radians } / \mathrm{sec}\)
\(\frac{4}{25} \text { radians } / \mathrm{sec}\)
\(\frac{1}{5} \text { radians } / \mathrm{sec}\)
\(\frac{1}{3} \text { radians } / \mathrm{sec}\)
Consider a game where the player tosses a six-sided fair die. If the face that comes up is 6, the player wins Rs. 36, otherwise he loses Rs. k2, where k is the face that comes up k = {1, 2, 3, 4, 5}.
The expected amount to win at this game in Rs. is
\(\cfrac { 19 }{ 6 } \)
\(-\cfrac { 19 }{ 6 } \)
\(\cfrac { 3 }{ 2 } \)
\(-\cfrac { 3 }{ 2 } \)
The random variable X has the probability density function
\(f(x)=\left\{\begin{array}{lr}
a x+b & 0<x<1 \\
0 & \text { otherwise }
\end{array}\right.\) and \(E(X)=\frac { 7 }{ 12 } \), then a and b are respectively
1 and \(\frac { 1 }{ 2 } \)
\(\frac { 1 }{ 2 } \) and 1
2 and 1
1 and 2
A computer salesperson knows from his past experience that he sells computers to one in every twenty customers who enter the showroom. What is the probability that he will sell a computer to exactly two of the next three customers?
\(\frac { 57 }{ { 20 }^{ 3 } } \)
\(\frac { 57 }{ { 20 }^{ 2 } } \)
\(\frac { { 19 }^{ 3 } }{ { 20 }^{ 3 } } \)
\(\frac { 57 }{ 20 } \)
The product of all four values of \(\left( cos\cfrac { \pi }{ 3 } +isin\cfrac { \pi }{ 3 } \right) ^{ \frac { 3 }{ 4 } }\) is
-2
-1
1
2
The value of \(\left( \cfrac { 1+\sqrt { 3 } i}{ 1-\sqrt { 3}i } \right) ^{ 10 }\) is
\(cis\cfrac { 2\pi }{ 3 } \)
\(cis\cfrac { 4\pi }{ 3 } \)
\(-cis\cfrac { 2\pi }{ 3 }\)
\(-cis\cfrac { 4\pi }{ 3 }\)
The general solution of the differential equation \(\log \left(\frac{d y}{d x}\right)=x+y\) is
ex + ey = C
ex + e-y = C
e-x + ey = C
e-x + e-y = C
P is the amount of certain substance left in after time t. If the rate of evaporation of the substance is proportional to the amount remaining, then
P = Cekt
P = Ce-kt
P = Ckt
Pt = C
The slope at any point of a curve y = f (x) is given by \(\frac{dy}{dx}=3x^2\) and it passes through (-1, 1). Then the equation of the curve is
y = x3 + 2
y = 3x2 + 4
y = 3x4 + 4
y = 3x2 + 5